Which of the following numbers is a factor of 187? ${5,7,9,10,11}$
Explanation: By definition, a factor of a number will divide evenly into that number. We can start by dividing $187$ by each of our answer choices. $187 \div 5 = 37\text{ R }2$ $187 \div 7 = 26\text{ R }5$ $187 \div 9 = 20\text{ R }7$ $187 \div 10 = 18\text{ R }7$ $187 \div 11 = 17$ The only answer choice that divides into $187$ with no remainder is $11$ $ 17$ $11$ $187$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $11$ are contained within the prime factors of $187$ $187 = 11\times17 11 = 11$ Therefore the only factor of $187$ out of our choices is $11$. We can say that $187$ is divisible by $11$.